Computation is the process of applying a procedure or algorithm to the solution of a mathematical problem. Mathematicians and physicists have been occupied for many decades pondering which problems can be solved by which procedures, and, for those that can be solved, how this can most efficiently be done. In recent years, quantum mechanics has augmented our understanding of the process of computation and of its limitations.

Perspectives in Computation covers three broad topics: the computation process and its limitations, the search for computational efficiency, and the role of quantum mechanics in computation. The emphasis is theoretical; Robert Geroch asks what can be done, and what, in principle, are the limitations on what can be done? Geroch guides readers through these topics by combining general discussions of broader issues with precise mathematical formulations—as well as through examples of how computation works.

Requiring little technical knowledge of mathematics or physics, Perspectives in Computation will serve both advanced undergraduates and graduate students in mathematics and physics, as well as other scientists working in adjacent fields.

AUTHOR BIOGRAPHY

Robert Geroch is professor in the Department of Physics at the University of Chicago and author of General Relativity from A to B and Mathematical Physics, both published by the University of Chicago Press.

REVIEWS

"A short, beautiful set of seminar lecture notes for physics graduate students on the theory of computing with an emphasis on the flowering field of quantum computing. Perspectives in Computation is not an encyclopedic treatment; the book’s references to the literature are sparse. Rather, it is a carefully constructed single story line presented with outstanding clarity. It contains few equations but many carefully conceived logical arguments. . . . The book is an eccentric and rewarding tour de force."

— William H. Press, Physics Today

TABLE OF CONTENTS

1 Introduction

2 Characters and Strings

3 Problems

4 Computability

5 Turing Machines

6 Noncomputable Problems

7 Noncomputable Numbers

8 Formal Mathematics

9 Difficulty Functions

10 Difficult Problems; Best Algorithms

11 A Language for Efficiency

12 Are There Better Languages?

13 Probabilistic Computing

14 Quantum Mechanics

15 Grover Construction

16 Grover Construction: Six Issues

16.1 Initial State

16.2 Final Observation on Hin

16.3 Building the Operator W

16.4 Building the Operator V

16.5 Errors

16.6 What Is the Problem?

17 Quantum-Assisted Computing

18 Quantum-Assisted Computability

19 Quantum-Assisted Difficulty Functions

20 Quantum-Assisted Efficiency I

21 Quantum-Assisted Efficiency II

22 Conclusion

References

Index

REQUEST ACCESSIBLE FILE

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Computation is the process of applying a procedure or algorithm to the solution of a mathematical problem. Mathematicians and physicists have been occupied for many decades pondering which problems can be solved by which procedures, and, for those that can be solved, how this can most efficiently be done. In recent years, quantum mechanics has augmented our understanding of the process of computation and of its limitations.

Perspectives in Computation covers three broad topics: the computation process and its limitations, the search for computational efficiency, and the role of quantum mechanics in computation. The emphasis is theoretical; Robert Geroch asks what can be done, and what, in principle, are the limitations on what can be done? Geroch guides readers through these topics by combining general discussions of broader issues with precise mathematical formulations—as well as through examples of how computation works.

Requiring little technical knowledge of mathematics or physics, Perspectives in Computation will serve both advanced undergraduates and graduate students in mathematics and physics, as well as other scientists working in adjacent fields.

AUTHOR BIOGRAPHY

Robert Geroch is professor in the Department of Physics at the University of Chicago and author of General Relativity from A to B and Mathematical Physics, both published by the University of Chicago Press.

REVIEWS

"A short, beautiful set of seminar lecture notes for physics graduate students on the theory of computing with an emphasis on the flowering field of quantum computing. Perspectives in Computation is not an encyclopedic treatment; the book’s references to the literature are sparse. Rather, it is a carefully constructed single story line presented with outstanding clarity. It contains few equations but many carefully conceived logical arguments. . . . The book is an eccentric and rewarding tour de force."

— William H. Press, Physics Today

TABLE OF CONTENTS

1 Introduction

2 Characters and Strings

3 Problems

4 Computability

5 Turing Machines

6 Noncomputable Problems

7 Noncomputable Numbers

8 Formal Mathematics

9 Difficulty Functions

10 Difficult Problems; Best Algorithms

11 A Language for Efficiency

12 Are There Better Languages?

13 Probabilistic Computing

14 Quantum Mechanics

15 Grover Construction

16 Grover Construction: Six Issues

16.1 Initial State

16.2 Final Observation on Hin

16.3 Building the Operator W

16.4 Building the Operator V

16.5 Errors

16.6 What Is the Problem?

17 Quantum-Assisted Computing

18 Quantum-Assisted Computability

19 Quantum-Assisted Difficulty Functions

20 Quantum-Assisted Efficiency I

21 Quantum-Assisted Efficiency II

22 Conclusion

References

Index

REQUEST ACCESSIBLE FILE

If you are a student who has a disability that prevents you
from using this book in printed form, BiblioVault may be able to supply you
with an electronic file for alternative access.

Please have the disability coordinator at your school fill out this form.